Waveguide



March 5, 1968 w. KRANK f-:TAL l `|3,372,352

WAVEGUIDE Original Filed Sept. lO, 1964 I5 Sheets-Sheet l Jnven/oltfwou-GANG K RANK sumen MOHRING MW fifa ATTORNEY March 5, 1968 w. KRANKETAL 3,372,352

WAVEGUIDE Original Filed Sept. l0, 1964 5 Sheets-Sheet 2 wwf-Hrw' .7nven fom WDLFGANGKRANK Bb/GLJNTER ATTORNEY March 5, 1968 1 w. KRANK ETAL3,372,352

WAVEGUIDE origina-11 Filed-sept. 10, 1964 5 sheets-sheet s Jnvenfm.'WDLFGANG K RANK GUNTER MP/R/ING BY ATTORNEYS United States Patent fice3,372,352 WAVE/GUIDE Wolfgang Krank, Backnang, Wurttemherg, and GnterMhring, Langenhagen, Hannover, Germany, assignors to TelefunkenPatentverwertungs-G.m.b.H., Ulm (Danuhe), and Hackethal-Draht undKabel-Werke ALG.,

Hannover, Germany Continuation of application Ser. No. 395,532, Sept.10, 1964. This application July 24, 1967, Ser. No. 655,672 3 Claims.(Cl. S33-95) ABSTRACT F THE DISCLOSURE gation pitch angle.

This application is a continuation of application Ser. No. 395,532,filed Sept. 10, 1964, now abandoned.

The invention relates to a waveguide of optimum dimensions which can bewound on a drum preferably for the wide-band transmission of linearlypolarized electromagnetic waves, and which comprises a metal tube ofoval cross section welded with a longitudinal seam, wherein the majorand minor raxes of the oval cross section, which are perpendicular toone another, vary, depending on the corrugations, along the longitudinalaxis of the waveguide.

It is known to use waveguides with differing crosssectional shapes forthe transmission of electromagnetic waves of very high frequency. Thesewaveguides generally have circular or rectangular cross section. Smoothwaveguides of oval cross section are lalso known.

For special applications (for example serial feeders of mobile stations)it is often necessary to have a fiexible waveguide, that is, a waveguidewhich can be wound on a drum which permits a satisfactory transmissionof linearly polarized electromagnetic waves. A waveguide of oval crosssection has recently been proposed for this purpose. It comprises acorrugated metal tube with a longitudinal weld seam. In this case, thetransmitted useful wave is a linearly polarized electromagnetic wave,the E-vector of which is perpendicular to the major axis of the ovalcross section.

The main object of the present invention is to provide a waveguide ofthe mentioned kind with optimum dimensions for a predetermined frequencyband.

Therefore, starting from a waveguide for the wide-band transmission oflinearly polarized electromagnetic waves, which can be wound on a drumand which comprises a corrugated metal tube of oval cross section whichis longitudinally welded and in which the major and minor axes of theoval cross section are perpendicular to one another and vary along thelongitudinal axis of the waveguide depending on the corrugation, it isproposed according to the invention that the lowest frequency to betransmitted in the given band is about higher than the limit frequencyof the useful Wave in the waveguide and the first interfering frequencylies above the highest -band frequency, and that the relationshipbetween the effective perpendicular axes of the cross section of theoval waveguide satisfy the following conditions:

3,372,352 Patented Mar. 5, 1968 :depth of corrugations in the directionof the major axis,

and

tFbi-b1 :depth of corrugations in the direction of the minor axis.

Additional objects and advantages of the present invention will becomeapparent upon consideration of the following description when taken inconjunction with the accompanying drawings in which:

FIGURE 1 is a schematic longitudinal sectional view of a waveguidehaving helical corrugations.

FIGURE 2 is a schematic longitudinal sectional view of a waveguidehaving a different type of corrugations,

FIGURE 3 is a schematic transverse sectional View of an oval corrugatedwaveguide.

FIGURE 4 is a schematic cross-sectional View through a portion of acorrugated waveguide wherein `the lengths of the ridges is the same asthe lengths of the grooves.

FIGURE 5 is a view similar to FIGURE 4 and wherein the lengths of theridges is less than the lengths of the grooves.

FIGURE 6 is a view similar to the previous two figures but wherein thelengths of the ridges is greater than the lengths of the grooves.

FIGURE 7 is a diagram showing in graphical form some relationshipsbetween different properties of ellipti# cal waveguides.

In general, the waveguide is constructed in such a Inanner that thelongitudinally welded metal tube is periodically corrugated, preferablywith helical corrugations. Such a periodically corrugated waveguide isillustrated in longitudinal section in FIGURE 1.

For special applications, fiexible waveguides are concervable which areoval in cross section and the corrugations of which do not runhelically. A longitudinal section through such a waveguide isillustrated diagrammatically in FIGURE 2.

FIGURE 3 shows a cross section of a corrugated flexible waveguide ofoval cross section. In this case, al designates the major axis of theunobstructed cross section, and a2 the maximum major axis of the ovalcross section due to the corrugations of the hollow tubular conductor.The minor axis of the unobstructed cross section is designated by b1 andthe maximum minor axis due to the corrugations is designated by b2.

A waveguide constructed according to the invention has optimumdimensions with regard to its flexibility, its attenuation, and/ or thebandwidth.

In practice, an oval waveguide of corrugated tube would scarcely be usedwith a ratio of the effective axes Zvw/aw of less than 0.4. The possibledimensions will be explained below with reference to FIGURE 7. Therelative frequency bandwidth, entered on the vertical axis in FIGURE 7,is plotted against the ratio formed from the effective minor axis bW andthe effective major axis aw. A distance of 20% (corresponding to thebroken line E) is assumed as a lower limit to the bandwidth, while thefirst interfering frequency which occurs is assumed as the upper limit.

This is indicated by the curved full line G in FIGURE 7. It iscalculated in accordance with the formula 1 Af: b 2 b -0.11 a-W +1.14.(f-0.0231

This curve can be modified somewhat for oval waveguides and thoseresembling an ellipse, the constant value of 0.0234 given in the aboveformula merely being corrected by adding or subtracting a certainamount. In the practical dimensioning, it is advisable not to go rightup to the upper limit (full curved line G) so that no reflection peaksmay occur in bent portions of the hollow conductor due to undesiredcoupling with higher mode waves. A distance of from about 2 to 5% ispreferably selected. In FIGURE 7, the broken curve F represents adistance of 2% from the first interfering frequency which occurs.Fundamentally, the lower frequency limit may also be brought moreclosely to the critical frequency of the useful wave, in which case theattenuation at the lower end of the band rises sharply as a result ofthe dispersion behavior of the hollow conductor. In FIGURE 7, a value of10% was assumed for this, represented by the parallel straight line D inphantom lines. If bandwidth Af of 10% has to be transmitted for example(see FIGURE 7, full vertical line C), then the hollow conductor has themaximum flexibility for a ratio bW/aw of 0.75. The waveguide thusdimensioned has not, however, optimum conditions with regard toattenuation. In order to achieve optimum attenuation, a ratio of theeffective axes bW/aW of 0.4 would have to be selected as shown by thefull vertical line A in FIGURE 7. An optimum waveguide with regard toattenuation and exibility is afforded, if the ratio bw/azW amounts toabout 0.6 as represented by the vertical line B in FIGURE 7.

If the required relative bandwidth Af is greater than 10%, then similarratios of bW/aW can be read off from FIGURE 7 in a similar manner.

The corrugations of the hollow conductor may vary in configuration. Thecorrugation is preferably effected, however, in such a manner that it isperiodic.

In a further development of the invention, the corrugations of thehollow conductor are constructed in such a manner that the distance Sbetween two successive ridges satisfies the condition and preferablyamounts to )1/5, in which A designates the mean free wave length inspace of the frequency band to be transmitted. In this case, thecorrugations are preferably helical.

If the cross section of the waveguide according to the invention isconsidered, then for each pitch S (see FIG- URES 4, and 6), the effectof a capacitive diaphragm is obtained in the vertical plane and that ofan inductive diaphragm in the horizontal plane. The frequencycharacteristics of these two elements are not exactly opposite so that aslight residual reflection occurs at each element. If the pitch isselected of the order of magnitude of M4, however, then the resultingvalue of the successive disturbance point is at a minimum with regard tothe reflection factor of the waveguide. If the pitch S is selectedsomewhat less than M4 with regard to the wavelength A, then although thereflection factor will increase somewhat, nevertheless it remains withintolerable limits if the pitch S does not drop below a value of 71/10.For the dimensioning, this means that if the pitch S lies between )1/ 10and M4, no sharp reflection peaks occur within the frequency band to betransmitted as a result of the residual reflections present. For asatisfactory transmission of a given frequency band, therefore, thecorrugation must be effected in such a manner that disturbing reflectionpeaks lie outside the frequency band. The above condition can also beexpressed by the wavelength of the hollow conductor. The specificationsfor the limits of S are met if 4 the pitch angle a of the corrugation(FIGURE l) is between 0 and 60. In corrugated hollow conductors of ovalcross section already produced the pitch angle was preferably 10.

For particular applications, the corrugation may also be such that thepitch angle a varies continuously between two given values (e.g., 10 and-|-l0) along the longitudinal axis of the waveguide.

The formula given hereinbefore, according to which the ratio between theeffective minor axis bW and the effective major axis aW should bebetween the values 0.4 and 0.8, contains corrective factors K1 and K2 aswell as the two quantities t1 and t2 which represent the depths of thecorrugations. According to the invention, the corrective factors K1 andK2 lie between the values -O.65 and +0.65. In general, the quantities t1and t2 may be different. For a rough calculation, however, it can beassumed that the depths of the corrugations t1 and t2 are approximatelyequal. For example, the following condition may apply to the depth ofthe corrugations:

On the basis of the above assumptions, it is possible to distinguishbetween three distinct forms of corrugations:

The form of corrugation illustrated in FIGURE 4 is constructed in such amanner that the length Z1 of the ridge is equal to the length Z2 of thegroove of a corrugation (S=Z1i-Z2), in which case the corrective factorsK1 and K2 have a value of approximately zero. In this figure,tdesignates the depth of the corrugation as defined above, while S isthe pitch. The quantities a1, b1, a2, b2 represent the correspondingaxes ofthe corrugated hollow conductor.

FIGURE 5 illustrates a further special case of a possible form ofcorrugation. In this case, the length Z1 of the ridge is greater thanthe length Z2 of the groove of the corrugation, in which case thecorrective factors K1 and K2 are different from zero and preferably havea value which is greater than zero. The magnitude of the correctivefactor depends on the penetration of the field vector of the transmittedwave into the corrugations of the hollow conductor. This means that thecorrective factor K1 or K2 is dependent not only on the dimensions Z1,Z2 and t, but also on the shape of the curvature of the corrugations.With the form of corrugation illustrated in FIGURE 5, the correctivefactors are positive.

In the example illustrated in FIGURE 6, the reverse case is assumed incomparison with FIGURE 5. The length Z1 of the ridge of a corrugation isselected shorter than the length Z2 of the groove in this case. In thiscase, too, the corrective factors K1 and K2 are different from zero andthey are negative. If the curvature of the corrugations is selecteddifferent from the example illustrated in FIGURE 6, then modificationsare conceivable in which the corrective factors, although different fromzero, may have a value greater than zero.

Finally, an example of dimensioning will be given in which the conditionis assumed that the relative bandwidth to be transmitted amounts to 20%and optimum flexibility is required. According to FIGURE 7, a ratio ofbW/aW of 0.676 is obtained for this. If it is assumed that the depth ofcorrugation t1 is different from the depth of corrugation t2 and theirratio (11/ t2) has the value 0.9, then, with the corrective factorsK1=0.03 and K2=0.015 because of the profile selected, the ratiosb1/a1=0.7 and b2/a2=0.65 are obtained. If the major axis a1, forexample, is given, then the dimensions of the waveguide can becalculated on the basis of the formula stated in columns l and 2. In anexample which was carried out in practice, the pitch S was selected as)1/5. The corrective factors K1 and K2, which are characteristic for theprofile selected, may be determined empirically.

It will be understood that the above description of the presentinvention is susceptible to various modifications, changes andadaptations, and the same are intended to be comprehended within themeaning and range of equiv- -alents of the appended claims.

We claim:

1. A waveguide of optimum dimensions in the form of a flexible hollowconductor for the wideband transmission of linearly polarizedelectromagnetic waves, comprising a corrugated metal tube of oval crosssection which is welded longitudinally, said waveguide havingcorrugations which are periodic and which are selected in such -a mannerthat the disturbing reflection peaks lie outside the frequency band tobe transmitted, the major and minor axes of the oval cross section beingperpendicular to one another and varying along the longitudinal axis ofthe waveguide depending on the corrugations, the lowest frequency to betransmitted in the given band being about 20% higher than the limitfrequency of the useful wave in the waveguide, and the ratio between theeffective perpendicular axes of the oval cross section of the waveguidesatisfying the following condition:

:the depth of the corrugations in the direction of the major axis;

t b2-b1 2" 2 :the depth of corrugations in the direction of the minoraxis;

and wherein the spacing (S) between two successive ridges of thecorrugations satisfying the condition:

in which x is the mean free wavelength of the frequency band to betransmitted; and the spacing between two successive ridges of thecorrugations being such that S=}\/5.

2. A waveguide of optimum dimensions in the form of a flexible hollowconductor for the wideband transmission of linearly polarizedelectromagnetic waves, comprising a corrugated metal tube of oval crosssection which is welded longitudinally, said tube being corrugated tohave helical corrugations whose pitch angle a is about the major andminor axes of the oval cross section being perpendicular to one anotherand varying along the longitudinal axis of the waveguide depending onthe corrugations, the lowest frequency to be transmitted in the givenband being yabout 20% higher than the limit frequency of the useful wavein the waveguide, and the ratio between the effective perpendicular axesof the oval cross section of the waveguide satisfying the followingcondition:

in which a1 is the major axis of the free cross-sectional area; b1 isthe minor axis of the free cross-sectional area;

6 a2 is the maximum major axis due to the corrugations; b2 is themaximum minor axis due to the corrugations; K1 is a corrective factorfor determining the effective major axis which depends on the shape ofthe profile of the corrugations; K2 is a corrective factor fordetermining the effective minor axis which depends on the shape of theprofile of the corrugations;

:the depth of corrugations in the direction of the major axis;

=the depth of corrugations in the direction of the minor axis.

3. A waveguide of optimum dimensions, in the form of a exible hollowconductor for the wideband transmission of linearly polarizedelectromagnetic waves, comprising a corrugated metal tube of oval crosssection which is welded longitudinally, the major and minor axes of theoval cross section being perpendicular to one another and varying alongthe longitudinal axis of the waveguide depending on the corrugations,the lowest frequency to be transmitted in the given band being about 20%higher than the limit frequency of the useful wave in the waveguide, andthe ratio between the effective perpendicular axes of the oval crosssection of the waveguide satisfying the following condition:

:the depth of corrugations in the direction of the major axis;

:the depth of corrugations in the direction of the minor axis;

wherein the corrective factors condition:

(K1 and K2) satisfy the and the depth of the corrugations (t1 and t2)are substantially equal and satisfy the condition:

the length of the ridges of the corrugations is greater than the lengthof the grooves of the corrugations, and the corrective factors (K1 andK2) are different from zero; said waveguide is dimensioned for optimumflexibility when the relative frequency bandwidth to be transmittedamounts to 20%; and the ratio of the effective '7 axes of the crosssection is 0.676, the ratio of the depths of the corrugations is 0.9,the pitch is M5 and the ratio of the free minor axis (b1) to the freemajor axis (a1) has the value 0.7 with a ratio (b2/a2) of the maximumminor axis to the maximum major axis of 0.65.

References Cited UNITED STATES PATENTS 3,200,256 8/1965 Schttlifel etal. 333-95 8 FOREIGN PATENTS 877,692 12/ 1942 France. 1,113,490 9/1961Germany.

739,488 11/ 1955 Great Britain.

OTHER REFERENCES Southworth: Principles and Applications of waveguideTransmission, Von Nostrand, 1950, pp. ISO-183.

HERMAN KARL SAALBACH, Primary Examiner.

